BEAM TECHNOLOGY

150

PART I V : SPECIAL TOPICS CHAPTER 13: BEAM TECHNOLOGY 1.

LASER

It is possible to produce a spot of extremely, high-power density by focusing a laser beam via a lens, due to the coherence of light. Hence, a laser light can be utilized as a non-invasive heat source in materials processing. The special features of laser processing include: (1)

Being non-invasive, its product is free from mechanical deformation and is not affected by material hardness.

(2)

Since a laser beam can easily propagate in air, material processing can be performed from a remote distance.

(3)

Even if the processing spot is near an element that can ill-tolerate thermal effects, it is possible to perform a pulse-type processing with a short heating time. This is because the regime of temperature rise is confined to a narrow section in the vicinity of the spot, with practically no ill-effect on the element.

(4)

Materials in an enclosed container can be processed through a transparent (such as glass) window.

(5)

Since power control is relatively easy, such a processing is superior in controllability and suitable for automation.

2. PRINCIPLES OF LASER PROCESSING A laser light source apparatus can produce an output beam which is characterized by the wavelength and directionality that are determined by the laser material of light oscillator. A spot with an extremely high power density can be produced by focusing this beam via a lens. Table 13-1 lists approximate mean power densities of some typical methods that have been employed in conventional processes. It reveals the magnitude of power densities in laser processing. When a laser beam irradiates the surface of the material to be processed, a substantial fraction of the light is reflected, with the remaining being absorbed by the material. Only the energy absorbed is useful in processing. Figure 13-1 depicts the relationship between the wavelength of irradiating lights and the absorptivity of irradiated materials. It is found that the energy absorptivity of these surfaces varies from 1 to 5% in the case of a CO2 laser and 2 to 40% for YAG laser. Both lasers are widely used in laser processing. The absorptivity is strongly dependent on the characteristics of the materials surface. When a surface is irradiated by a laser beam, the temperature at the irradiated point rises and the surface characteristics

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change, resulting in an increase in absorptivity. When melting occurs at the irradiated point, the absorptivity further increases. Heat transfer phenomena occur in the course of laser processing. It is seen in Fig. 13-2 that the power density distribution exhibits a Gaussian distribution curve as

process

power

soldering machine cutting c a r b o n a r c w e l d i n g 75V-220A 20V-200A electric welding solar surface machine grinding lOOkV-10mA electron beam lkW laser b e a m

radius (mm)

10 10

0.1 0.1

power density 2 (W/m ) 0.4 6 2xl0 6 5xl0 7 5xl0 7 7xl0 8 2xl0 11 lxlO 11 lxlO

Table 13-1 Comparison of power density for various processes „ polished silver +->

;gα ο

m &

cd

0.2^ 0.4 0.6 1\ 2 excimer YAG wave length [//m] Figure 13-1 Absorptivity-wave length relationship for various metalic materials -2r2' I(r)=-8E-exp 2 πd

(13-1)

(when the beam irradiates a sufficiently large surface). Here, Ρ denotes the light power [W] and r is the radial distance from the beam center [m]. 2(d/2) represents the beam radius, and is defined at the radial location where the intensity is 1/e ( = 0.135) of the center intensity. The timewise temperature variation T(r,z,t) at each point in the material after the initiation of laser irradiation can be obtained by solving the unsteady, axisymmetrical, two-dimensional heat conduction equation. The temperature at the central point of the material surface To(t) = T(0,0,t) is obtained as a function of time as (Ready, 1971):

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(13-2) Here, a is the absorptivity and k and α are the thermal conductivity [W/mK] and thermal 2 diffusivity [m /s] of the surface, respectively. Equation (13-2) is obtained under the conditions of constant material properties and constant surface shape (in the absence of melting).

Figure 13-2 Irradiation of a body by a laser beam with Gaussian-type intensity distribution

Figure 13-3 Relationship between metalic surface temperature and laser irradiation time

time

Tj : transformation point Τ2 : melting point T 3 : boiling point

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Figure 13-3 illustrates schematically the temperature rise at the irradiated point of a laser beam on a steel surface. For a short time after the initiation of irradiation, the temperature increases following Eq. (13-2) and then hesitates momentarily at the transformation point, Ti (about 750° C). This is because of an increase in the specific heat according to a change in the crystal structure in the material. This stage can be utilized for transformation hardening of the material. For a sufficiently strong laser intensity , the temperature further increases and reaches the melting point T 2 (about 1,350° C) where the material melts. This phenomenon can be utilized in welding. If irradiation is continued, the temperature reaches the boiling point, T 3 , and the material evaporates. This phenomenon can be used in drilling and cutting. Under a very high power density, the evaporated material transforms into a plasma, as in Fig. 13-4. It is unclear whether the presence of plasma would promote or obstruct material processing (Yang et al., 1992). The above process is completed in 0.1 to 10 μ8 after the initiation of irradiation. If the power intensity of the laser beam is not so high, the energy input to the irradiated point may balance the heat losses due to conduction, convection or radiation to the other parts of the material and its surroundings, resulting in saturation of the temperature elevation at a certain level. It is known that the energy density of a laser beam, I, and the irradiation time must be uniquely determined for each application. Figure 13-5 plots the laser power density against irradiation time for various applications. Table 13-2 lists applications of various type lasers in practice.

Figure 13-4 A schematic of laser machining

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Laser irradiation time

[s]

Figure 13-5 Power density versus laser irradiation time in various laser machining

3. THEORY ON LASER PROCESSING The phenomena occurring in laser processing are extremely complex due to the coexistence of (1) energy transport by conduction and radiation, (2) transfer of energy and momentum by convection, and (3) mass transfer. In a special case where conduction is the dominating mechanism, the problem may be simplified to obtain its analytical solution (Ready, 1971; Carslaw and Jaeger, 1959; Gregson, 1983; Sandven, 1979; Cline and Anthony, 1977). However, in many instances, a physical model is established and an attempt is made to numerically solve the corresponding governing equations (e.g., Mazumder and Steen, 1980; Chan et al., 1987; Basu and Srinivasan, 1988). Here, consideration is given to the case where, upon the irradiation of a laser beam, the irradiated point on the surface undergoes melting, but not evaporation (with an application to transformation hardening). Numerical computations will be performed on a very simplified circumstance. Consider a continuous-wave laser beam irradiating a surface which absorbs it with a Gaussian type distribution, as depicted in Fig. 13-6.

155

w a v e length [/mi]

laser type

YAG gas lasers

glass

C02

solid state lasers

1.06 (0.53) (0.266)

1.06

10.6

power

application

continuous (—1.5 kW)

cutting soldering brazing

Q-switching ( - 5 0 W) ( 5 0 - 1 0 0 ns)

scribing trimming marking annealing

pulsed ( - 1 0 0 J) (20 — 50 ms) pulsed ( - 1 0 0 J) (0.2 — 8 ms)

drilling cutting welding

continuous ( - 2 0 kW)

cutting welding

pulsed (—10 kW) (0.1 ms)

drilling spot welding

drilling cutting welding marking scribing

Ar

+

excimer

0.49 0.51 0.19 0.25 0.31 0.35

continuous ( - 4 0 W) (ArF) (KrF) (XeCl) (XeF)

pulsed (—40 W) pulsed ( - 1 0 0 W) pulsed (—65 W) 100 Hz ( - 8 W)

plating annealing mask repairing pattern generating pattern generating surface reforming abrasive process

Table 13-2 Lasers and their applications

156

2

2

/(r)=/ 0 exp[-2r /(d/2) ]

Figure 13-6 A physical model for surface melting by means of laser irradiation A portion of the surface centered at the irradiated point (r = 0) melts, and a steady state prevails there. It is postulated that (1) the melt is a Newtonian fluid, (2) surface tension gradients at the gas-liquid interface induce flow in the melt, (3) transport phenomena are axisymmetric, and (4) physical properties of both the solid and liquid phases remain constant, but that the surface tension of the melt is a function of temperature. Under these assumptions, the continuity Navier-Stokes and energy equations read: Continuity equation: ^ + ü + 3v=o 9r r 3z Navier-Stokes equations:

(13-3)

dt

du dr

du dz

3v 3t

3v 3r

d\\

dp

ίθ ν

dzj

dz

\dr

idu

(13-4)

-rr-+U^— + V^r-

2

2

d^vX

ι dv r dr

2

dz

„_

(13-5)

Energy equation: pC.

9T

IdT

j J T L f c i j U ΘΤ\

" i ä r ä r - a dzj zj + u

+ v

rlarrar)

d_l 3TV T

dz\ dz[

(13-6)

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The appropriate boundary conditions are

r = 0:

u = 0, ^ = 0, ^ = 0 dr dr

(13-8)

r = ro and Z = ZQ:

T = TOO

(13-9)

Numerical computations are performed using the thermo-physical properties of steel listed in Table 13-3.

Property Solidus Temperature Liquidus Temperature Density Thermal conductivity of solid Thermal conductivity of liquid Specific heat Latent heat Dynamic viscosity Volumetric expansion coefficient Temperature coefficient of surface tension

Value 1523 1723 7200 31.39 15.48 753 247 0.006 4 10" 6 10"

Κ Κ 3 kg/m W/mK W/mk J/kgK kj/kg Pa»s 1/K N/mK

Table 13-3 Thermo-physical properties of steel A representative result is demonstrated in Fig.8 13-7 (Ravindran et al., 1990) for the maximum 2 absorbed energy density of Ιο = 10 [W/m ] and the laser beam radius of d/2 = 3 [mm]. It is observed in Fig 13-7 (a) that the melt region is slightly larger than the laser beam radius and a large recirculating cell exists inside the melt. Figure 13-7 (b) presents the corresponding isotherms. In actual processing, the phenomena are mostly unsteady, the thermo-physical properties of both the solid and liquid phase are temperature-dependent, and the gas-liquid interface is not necessarily flat. In other words, the real situation may substantially deviate from the postulations made for the numerical analysis, and the results shown in Fig. 13-7 may differ considerably from reality. However, in view of the difficulties of experimental measurements, numerical computations using a high-speed, large-capacity computer can be a powerful tool in this study, provided that various conditions are modified to accommodate reality.

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(a)

(b)

Flow pattern

Isotherms

Figure 13-7 Surface-tension driven flow pattern and temperature distribution inside a melt

4.

ELECTRON BEAM

When an electron beam irradiates a material surface, the kinetic energy of electrons is converted into thermal energy or heat. In a vacuum, the power density may be increased by reducing the beam diameter through an electromagnetic force. When a material surface is irradiated by an electron beam of diameter d and current I, which is accelerated by a voltage V, its power density Ρ can be expressed as

159

P

=

_VL

(13-10)

\ 4 ; The power density of electron beams in use range from 1 to 100 MW/cm . For example, when an electron of 100 keV strikes an iron surface, it penetrates approximately 2.5 μπι and then converts into heat. Since an electron beam is small in size, if an uniformly distributed beam power, Q, of diameter 2R charges continuously through the surface of a semi-infinite body, the temperature distribution will vary with time as 2

(exp(^z)erfcf—^ T(r,z,t) =

2k{nR)

X(at) , . 1/2

• e x p ^ z W — ζ _1 /2 + λ(αί) 1 l λ [2(at) 1/2

Here, r denotes the radial distance; z, penetration depth; t, time; k, thermal conductivity; and a, thermal diffusivity. J o and J i are the Bessel functions of the zeroth and first orders, respectively, and are defined as

JjM=I

+2n

(13-12)

~o n! I^j + n + 1)

erfc(x) = 1 - erf(x) = 1 - - i - Ι expU') αξ = 1 π

ι/2 J

π

ι / 2

^

£ 0

"

( 1 13 3 )

(

2 n + 1 n !

)

It is worthwhile to explore the special features of beam work, as a local work, in the following: After a sufficient time elapses, Eq. (13-11) gives the surface center temperature, T o , to be Q/(2nRk). The time t o at which the surface center temperature reaches 0 . 8 4 T o is found to 2 be πR /a. Equation (13-9) also yields T(r,o,t 0)=0.25 T 0 T(0,R,to) = 0.29T 0 Hence, when the surface center temperature reaches 1,600° C, which is above the melting point of iron, i.e. 1,500° C, the temperatures at r = R and ζ = R achieve approximately 4 8 0 ° C. The local temperature gradients at the instant t o are (0.6 q/k) at r = R and (0.55 q/k) at ζ = R, 2 where q represents the power density, Q/(nR ). It means that the temperature gradients at the moment of t = t o are proportional to the power density, but are inversely proportional to the thermal conductivity. The temperature profiles obtained from Eq. (13-11) are graphically illustrated in Fig. 13-8.

160

Τ To

R

Ο.Ο8Τ0

Center 2R 4R

Distance

Beam diameter

Figure 13-8 Temperature distribution inside a semi-infinite body heated by a continuous electron beam In general, it is often difficult to perform cutting or grinding work on a material of low thermal conductivity, because the temperature at the working location is raised. For example, stainless steels of high nickel content are considered materials of difficult machining. The conditions suitable for electron beam work are nearly opposite to those for machine work. That is, it is easier to work on a material of low thermal conductivity because of difficulty in heat dissipation into the surroundings, resulting in a higher center temperature. The actual power density takes the form of the Gaussian distribution, as (13-14) where, σ denotes the standard deviation. Pittaway (1963) treated, in detail, temperature rises induced by stationary and moving electron beams. In reality, however, the working mechanisms induced by an electron beam are more complicated due to the penetration of its power density, most of which is absorbed by the material and converted into heat. The heatabsorption distribution differs with the distance from the material surface. More specifically, the maximum penetration range, L (cm), that an electron beam pierces through the material can be expressed as (Schwarz, 1964) L

- 2.76 χ 10-" A E pz

8 /9

5 /3

(l + 0-978 x 1 0 E )

5 73

xlO^E)

4 73

6

(l + 1.957

(13-15)

Here, ρ is the material density (g/cm ); E, energy (eV) of the incident electron; A, atomic weight; and z, atomic number. For example, when an electron of 100 eV strikes an iron plate, the penetration range is 25 μπι, as compared to a penetration range of 60 μπι in the case of aluminum. The maximum penetration range implies not a distance where an incident electron would stop, but the penetration location where the resulting heat generation is at a maximum. 3

161

Accordingly, the material temperature is at a maximum at the maximum penetration range, causing not only the metal to melt, but also to rapidly evaporate. It is conceivable that the pressure induced by such a rapid evaporation would blow away the surrounding melt. If a continuous beam is employed to irradiate a material, it would heat up not only the portion being irradiated, but also its neighboring parts. In order to avoid raising the temperature in the neighborhood of the workpiece, a pulse-type electron beam can be used for irradiation. For example, a 300 μπι-width belt-type beam irradiated5 zirconium (which has a melting point of 2 3 1,845° C) has pulse widths of 10~ s, 10" s, and 10" s at a frequency of 50 Hz repeating at one-second intervals. Figure 13-9 depicts the resulting temperature distribution when the power density is adjusted for the maximum temperature to coincide with each melting point (Miyazaki and Taniguchi, 1970). It is seen that machining in the form of beam width can be achieved by heating with a short pulse width at a high power density, followed by a long cooling time. This method is effective in enhancing the accuracy of machining dimensions.

Zirconium Period : 20ms B e a m width : 0.3mm

0.1 0.15 0.2

0.3

0.4

0.5

Distance from the beam center cm

Figure 13-9 Temperature distribution inside a zirconium heated by a pulse-type electron beam with various pulse widths

5. ION BEAM In contrast to electrons which constitute cathode rays and beta rays, and are emitted by hot bodies, an ion is an electrically charged atom or group of atoms. A free electron may attach itself to another molecule to form a negative ion. In gases, a molecule may lose an electron, as by the action of x-rays, to become a positive ion. Only focused ion beams are useful for machining in industrial applications. Table 13-4 presents ion sources for focused beams. The brightness, source size, energy and species of a duoplasmatron, gas phase ion source and liquid metal are compared in the table. Figure 13-10 depicts variations of the sputter rate with ion incidence angles for Cu and two Si's (100) and (111). All three materials exhibit a peak value of the sputter rate at an angle between 60 and 70 degrees beyond which the sputter rate falls steeply with a further increase in the angle of incidence.

162

Table 13-4 Ion sources for focused beams Duoplasmatron 2 2 10 A/cm sr

Brightness

Gas phase ion source 9 10

Liquid metal 6 10

Source size

50 μπι

10A

300A

Energy spread

4eV

leV

5-10 eV

Species

Ar and others

H^,He

+

0 1 0

+

Ga, Au, Be, Si, Pd, Β, P, As, Ni, Sb,

.

.

I

30

60

90

Ion incidence angle

deg

Figure 13-10 Variations of sputter rate with incidence angle of an ion beam for Cu, Si (100) and Si (111) Three typical functions of an ion beam are illustrated in Fig. 13-11 for material removal, doping implantation and deposition of a material. 6.

ELECTRICAL DISCHARGE

Electrical discharge machining was initiated in 1943 by Lazarenko, who developed a circuit for electrical discharge. Currently, both die-sinking electrical discharge machining and wire electrical discharge machining are popular. The principle of electrical discharge machining is to apply a voltage between an electrode and a workpiece in order to generate an electrical

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discharge phenomenon at a location of the shortest distance between the two, thus melting the surface of the workpiece by electrical discharge and finally removing the melt through evaporation. When both the workpiece and the electrode are immersed in a dielectric liquid, the central part of electrical discharge reaches 3,500° C to 18,000° C, and the released heat abruptly evaporates the liquid, inducing an impact force to blow away the melt portion. It was experimentally verified that the maximum value of the force being generated at that instant was about several hundred Newtons, depending upon machining conditions. In the case of machining iron, pits are of the order of 0.1 mm and the surface area of bubbles generated in the 2 liquid due to electrical discharge is generally smaller than 1 mm . That would induce a pressure of several hundred MPa, which is powerful enough to remove the molten metal. Let us examine the principle of machining from the viewpoint of electrical discharge phenomena. In general, machining is performed with the electrode as a cathode and the workpiece as an anode. An application of voltage between the two causes a dielectric

Ion beam miling

Ion beam

Material Removal

Doping Implantation

Deposition of material

Figure 13-11 Three typical functions of an ion beam

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breakdown, resulting in an ejection of electrons from the cathode which collide with neutral particles to induce ionization, thereby increasing the number of electrons. The electrons are accelerated by the electric field as they move toward the anode. As these cathode-ejected electrons move closer to the anode, an ionization of neutron particles causes an increase in the number of electrons. This phenomenon is called electron avalanche. Both the number of electrons and the current increase with an increase in the voltage. These phenomena are schematically illustrated in Fig. 13-12.

(c) Bubble of vapour expands and collapses

(d) Break down

Figure 13-12 Mechanisms of electric discharge In actual electrical discharge machining inside a liquid, the shortest distance between the electrode and the workpiece is several to several ten mm. The gap between the two is widened with an increase in the concentration of debris in the dielectric fluid resulting from machining. The discharge duration is 1 to 1 ms. Machining is performed by repeating electrical discharges from several thousand to several hundred thousand times per second. Figure 13-13 depicts voltage variations in one cycle consisting of the electric-discharge duration time, ton, the delay time between dielectric breakdown and electrical discharge, td, and the resting time after electrical discharge ends and before dielectric restoration, toff. The duty factor, df, is defined as df =

^

ton + td + toff

(13-14)

The working capability can be enhanced by increasing the duty factor. If df is too large, toff may become to short, triggering a new discharge before the complete dissolution of the ions

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width Figure 13-13 Voltage variations in one cycle of electric discharge generated during the previous discharge. It may result in an abnormal discharge state with electrical discharges occurring at the same location, and consequently electrical discharge machining cannot be continued. A local concentration of electrical discharges causes an increase in the concentration of debris, which in turn invites more concentrated discharges, proceeding toward an abnormal discharge. In die-sinking electrical discharge machining, the debris concentration rises in the vicinity of discharges while the distance between the electrode and the workpiece is reduced. A method is developed by premixing powders (such as aluminum or graphite) into the dielectric liquid in order to maintain a uniform discharge without a substantial change in the debris concentration (Narumiya et al., 1989); Mohri and Higashi, 1991). It was reported that under the same working conditions, an addition of powders reduced surface roughness from 2.5 μπι to 0.8 μπι. Another way of improving surface roughness is by shortening ton to reduce both the depth and diameter of craters produced by electrical discharges. Electrode depletion during electrical charge machining occurs because of heating caused by an impact of positive ions. Generally, graphite and copper are selected as electrode materials because of their low electrode depletion and good workability. Their electrode depletion is low because graphite can sustain high temperatures while copper has a high thermal diffusivity, although its melting point is lower than that of steels. Kerosene is commonly employed as a dielectric liquid. It was reported that an addition of water into kerosene reduces the arc column diameter, but increases the current density by 50% (1.5 that of kerosene). In wire electrical discharge machining, water is commonly employed as the dielectric 2 liquid for prevention of fire hazards. Current working speed is 300 m /min (faster cases), with

166

a working precision of 1 to 2 μιτι. Wires are made of brass or copper. It differs from the diesinking electrical discharge machining in the use of new electrodes without considering electrode depletion. In order to prevent vibration due to forces induced by discharges, wires are stretched under a tension of 50 to 80% of breaking stress. The wire functions as a cathode and the workpiece as an anode. The pulse width is shorter (order of ms) than that of die-sinking electrical discharge machining. Breaking wire phenomenon due to concentrated discharges used to be a problem in the wire electrical discharge machining. Remedies include accelerating wire movement speed and supplying a sufficient supply of dielectric liquid to the working spot. No consideration is given to a new approach from a thermal viewpoint. In summary, like laser machining, electron beam machining, and other machining processes, electrical discharge machining is a kind of thermal machining. The process of thermal machining involves heating a workpiece in a working fluid. Nevertheless, no effort has been directed to thermal analysis, except to measure heat flow into the workpiece. The formation of craters is not an instant event It is recently disclosed that a small crater is first formed in a spiral shape, followed by growth. Detailed information requires further studies in the future.

7.

REFERENCES

Basu, B. and Srinivasan, J., 1988, "Numerical Study of Steady - State Laser Melting problem," Int. J. Heat Mass Transfer, Vol. 31,2331-2338 Carslaw, H. S. and Jaeger, J. C , 1959, "Conduction of Heat in Solids," Conduction of Heat in Solids, 2nd. ed. Oxford Univ. Press Carslaw, H.S. and Jaeger, J.C. (1959), Conduction of Heat in Solid, Oxford, p. 264. Chan, C. L., Mazumder, J. and Chen, M. M., 1987, "A Three-Dimensional Axisymmetric Model for Convection in Laser Melted Pool," Mat Sei. Engineering, Vol.3, 306-311 Cline, Η. E. abd Anthony, T. R., 1977, "Heat Treatment and Melting Material with a Scanning Laser or Electron Beam," J. Appl. Phys. Vol.48, 3895-3900 Gregson, V., 1983, "Laser Heat Treatment," Laser Materials Processing, ed. M. Bass, North Holland Mazumder, J. and Steen, W. M., 1980, "Heat Transfer Model for CW Laser Materials Processing," J. Appl. Phys., Vol.51, 941-947 Miyazaki, T. and Taniguchi, N. (1970), "Analysis of the Temperature at Electron and Laser Beam Processing," Precision Engineering, Vol. 36, No. 1, pp. 21 - 27 (in Japanese). Mohri, N. and Higashi, M. (1991), "A New Process of Finishing Machining on Free Surface by EDM Methods," Annals of CIRP, Vol. 40, No. 1, pp. 207 - 210. Narumiya, H. and Saito, N. (1989), "EDM by Powder Suspended Working Fluid," Proceedings of the 9th International Symposium for Electro-Machining, pp. 5 - 8 . Pittaway, L.G. (1963), "Temperature Analysis at Electron Beam Processing," Proceedings of the Electron Beam Symposium 5th Annual Meeting, March 28 - 29, pp. 264 - 272.

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Ravindran, Κ. Raghu Rama Rao, S. V., Marathe, A. G. and Srinivasan, J., 1990, "Numerical Studies on Laser-Melting," Proc. of Int. Symposium on Manufacturing and Materials Processing, Dubrovnik, Yugoslavia Ready, J. F., 1971, Effects of High-Power Laser Radiation, Academic Press, Ν. Y. Sandven, Ο. Α., 1979, "Heat Flow in cylindrical Bodies during Laser Transformation Hardening," Proc. SPIE, Vol. 198, 138-143 Schwarz, Η. (1964), "Mechanism of High Power-Density Electron Beam Penetration in Metal," Journal of Applied Physics, Vol. 35, No. 7, pp. 2020 - 2029. Yang, W.-J. et al. (1992), "A Study on Metal Melting Process by Laser Heating," Heat and Mass Transfer in Material Processing (eds. I Tanasawa and N. Lior), Hemisphere, Washington, D.C., pp. 53 - 63.